Question: Given $ m \angle ABC = 9x - 1$, $ m \angle CBD = 6x + 58$, and $ m \angle ABD = 87$, find $m\angle ABC$. $B$ $A$ $D$ $C$
Solution: From the diagram, we see that together ${\angle ABC}$ and ${\angle CBD}$ form ${\angle ABD}$ , so $ {m\angle ABC} + {m\angle CBD} = {m\angle ABD}$ Substitute in the expressions that were given for each measure: $ {9x - 1} + {6x + 58} = {87}$ Combine like terms: $ 15x + 57 = 87$ Subtract $57$ from both sides: $ 15x = 30$ Divide both sides by $15$ to find $x$ $ x = 2$ Substitute $2$ for $x$ in the expression that was given for $m\angle ABC$ $ m\angle ABC = 9({2}) - 1$ Simplify: $ {m\angle ABC = 18 - 1}$ So ${m\angle ABC = 17}$.